Reconstructing Human Pose from Inertial Measurements: A Generative Model-based Compressive Sensing Approach

The ability to sense, localize, and estimate the 3D position and orientation of the human body is critical in virtual reality (VR) and extended reality (XR) applications. This becomes more important and challenging with the deployment of VR/XR applications over the next generation of wireless systems such as 5G and beyond. In this paper, we propose a novel framework that can reconstruct the 3D human body pose of the user given sparse measurements from Inertial Measurement Unit (IMU) sensors over a noisy wireless environment. Specifically, our framework enables reliable transmission of compressed IMU signals through noisy wireless channels and effective recovery of such signals at the receiver, e.g., an edge server. This task is very challenging due to the constraints of transmit power, recovery accuracy, and recovery latency. To address these challenges, we first develop a deep generative model at the receiver to recover the data from linear measurements of IMU signals. The linear measurements of the IMU signals are obtained by a linear projection with a measurement matrix based on the compressive sensing theory. The key to the success of our framework lies in the novel design of the measurement matrix at the transmitter, which can not only satisfy power constraints for the IMU devices but also obtain a highly accurate recovery for the IMU signals at the receiver. This can be achieved by extending the set-restricted eigenvalue condition of the measurement matrix and combining it with an upper bound for the power transmission constraint. Our framework can achieve robust performance for recovering 3D human poses from noisy compressed IMU signals. Additionally, our pre-trained deep generative model achieves signal reconstruction accuracy comparable to an optimization-based approach, i.e., Lasso, but is an order of magnitude faster

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under PolyakL jasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analysis for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the respective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications

Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the guaranteed convergence of the algorithm. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods in a variety of image reconstruction problems in practice

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more